Nikkei Stock Average Volatility Index
Real-time VersionIndex Guidebook

Nikkei Inc.

・ With the modification of the methodology of the Nikkei Stock Average Volatility Index as Nikkei
Inc. (Nikkei) starts calculating and publishing it on the real-time basis since January 30, 2012,
which had been calculated on the end-of-day basis since November 2010, Nikkei drew up the Index
Guidebook of the Nikkei Stock Average Volatility Index Real -time Version. It would be changed
or modified corresponding to the revision of the index calculation rule etc in the future.
・ Copyright of this document is owned by Nikkei, and any copies, reprint s and reproduction of thisdocument are prohibited without the prior approval of Nikkei. This document is prepared solely forthe understanding of the index that Nikkei calculates and publishes, and it is not to be construed
as a solicitation or an offer to buy or sell any securities or related financial instruments.
・ This English document is a translation of the original document in Japanese and may not be an
entirely accurate translation of the original Japanese document. In any case where differences ari se
between the English version and the original Japanese version, the original Japanese document willprevail.

(May 29, 2023 version)

GB-145-E-20230529

1: Concept
Prices traded on option markets are usually determined, among others, by the volatility of
its underlying asset. From this price formation, in the calculation of the Nikkei Stock
Average Volatility index, the volatility expected by investors is inferred from the option
prices (premiums) in the markets.
A method widely used to estimate the fair variance rate in trading a variance swap etc onthe OTC market is used in the index calculation.
2: Index Calculation(1)Basic Points
・The index value is expressed as the figures rounded to two decimal places. Unit of theindex value is “points”.
・Use the prices of the Nikkei 225 futures and Nikkei 225 options (excepting mini options)on the Osaka Exchange (OSE), which the OSE publishes as the future and option prices
respectively.
・The index is calculated every 15 seconds during the day session of the Nikkei 225
options on the OSE (excluding the pre-closing) from Monday through Friday exceptJapanese national holiday. The index starts to be calculated from 15 seconds after the endof the opening auction usually 15 seconds past 9 A.M., and it is also calculated at the endof the closing auction.
・Cover the near-term (the first-term) option and the next-term (the second-term) option .
The options to calculate the index are rolled to the next delivery month on one business
day before the last trading date of the near-term option. Also cover the near-term (the firstterm) future (excepting mini futures and micro futures), and the future is rolled to thenext-term future on one business day before the last trading date of the near-term future.
(2)Selection of the prices
The prices of the futures and options used for the calculation are selected in the following
order of the priority.
①Latest traded price in for the past 15 seconds ( however, at the end of the closing auction,a traded price obtained when the orders are matched by so called “Itayose” method )②Middle price of best bid and best ask at the time of the calculation ( every 15 seconds )while the orders are matched by the so called “Zaraba” method ( however, at the end of
the closing auction, the middle price of best bid and best ask after the orders are matchedby the “Itayose” method (*1)③Last traded price of today’s session at the time before the past 15 seconds ( including
the night session on the previous business day )Copyright 2023 Nikkei Inc. All rights reserved.

2*1: Best bid and best ask prices to compute a middle price are invalid in cases that 1)best bid price is lower than orequal to 10yen and the difference between the best bid and best ask is greater than or equal to 4yen, 2)best bid priceis greater than 10yen and best ask is greater than best bid by 30% or more, 3) best ask is lower than or equal to bestbid.

(3)Formula
The Nikkei Stock Average Volatility Index is calculated in accordance with the following
procedure.
①Calculate the volatility  1,t based on the near-term (first-term) option at a time oft , and the volatility  2 ,t based on the next-term (second-term) option at a time of t .

Ti : the expiration date of i th-term option ( 9:00:00am on SQ date ) (*2)
Y365 : the number of seconds in a year on 365 day-basis (31,536,000 seconds )Li,t : Tokyo Term Risk Free Rate 1 month (TORF) on the previous business day (*3)
K i , j ,t : j th lowest Strike price (i.e. ascending order) of i th-term option at a time of t
: Closing price of put option with the expiration date of Ti at a time of t
: Closing price of call option with the expiration date of Ti at a time of t(however,(*4))

Ft : the price of the near-term future at a time of tp t : minimum j satisfying Ft  K i , j ,tqt : j minimizing the absolute difference between Ft and K i , j ,t at a time of t (*5)
ni ,t : the number of strike prices of i th-term options using for the calculation at a time of t (*6,*7)(however,)*2: the term to the expiration date is measured on the second time scale.
*3: In case that the TORF was not published for any reason, use the TORF rate previously available on the nearestday.
*4: For the option price whose strike price is nearest from the future price at a time of t , use the adjusted value
calculated from the put option price and call option price at the strike price. In addition,

andare put option price and call option price at strike price of K i ,qt ,t and the expiration date of Ti
at a time of t .
*5: If Ft ＜ K i , qt ,t ,then qt ＝ p t and if Ft  K i , qt ,t ,then qt ＝ pt -1*6: Use out-of-the-money (OTM) traded options (which have some volume) where the future price at the time ofthe calculation is defined as at-the-money (ATM). However, the options whose prices are invalid at the time of theCopyright 2023 Nikkei Inc. All rights reserved.

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calculation are treated as if these strike prices are not set (including cases by the Trading Suspension and theImmediately Executable Price Range Rule).
*7： In case that at the 17th or more strike prices from the ATM, the option prices at three consecutive strike prices(hereinafter called “Tri-strike Prices”) are invalid or are less than or equal 1 yen, the prices of put options at lower
strike prices than Tri-strike Prices and the prices of call options at higher strike prices than Tri-strike Prices are notused for the calculation even if these options are traded with some volume.

Please note that the option prices atTri-strike Prices are used for the calculation even if the prices are less than or equal 1 yen.

②Obtain the index value by linear interpolation of  1,t and  2,t to make the time toexpiration 30 days (*8,*9,*10)

Index Value

M : the number of seconds in 30 days (2,592,000 seconds)*8: If the term to expiration date is longer than 30 days, the index is calculated by liner extrapolation.
*9: As a result of the liner extrapolation, in case that the index value become s imaginary number ( meaning that theresult for the square root becomes negative ), the index value is calculated at a time of t

by using  1,t −1 and 2,t −1 used for the calculation at a time of t -1 (just before the calculation of this time), instead of  1,t and  2,t( however, at the first calculation of the day, use closing price on the previous day)*10: In the calculation of i th-term option at a time of t , 1)in case that the number of the strike prices whose
option prices are valid is 0 or 1, or 2)in case that the price of near-term future is invalid,  i,t at a time of t
not calculated, and the index value at a time of t

isis calculated by using  i ,t −1 which is used just before thecalculation of this time, instead of using  i,t (however excluding in case of “3:Miscellaneous (3)In case the Circuit
Breaker Rule is applied linked to Nikkei 225 Futures ”).

3: Miscellaneous(1)Previous and Retroactively Calculation in the past
From the commencement date of the calculation (November 19, 2010) to January 27, 2012,
the index was calculated on the end-of-day basis. And the index was calculated
retroactively dating back from June 12, 1989 to November 18, 2010 by the same end-ofday basis method.
Also from the commencement date of the calculation to December 10, 2021, the index wascalculated by using Euroyen LIBOR.
(2) Modification of the index value
If any event which affects the index value occurs (e.g. correction of the option or futures
prices published by the OSE), as a general rule, retroactive calculation for themodification will not be conducted.

Copyright 2023 Nikkei Inc. All rights reserved.

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(3) In case the Circuit Breaker Rule is applied linked to Nikkei 225 Futures
In case that all trades of the Nikkei 225 futures and Nikkei 225 options are halted by theCircuit Breaker Rule linked to Nikkei 225 futures, Nikkei shall halt the updating of theNikkei Stock Average Volatility Index. The complete trading suspensions of the OSE
caused by its system failure etc., is treated as the same above.
4: Others(1)Licensing
Nikkei Stock Average Volatility Index is an intellectual property that belongs to Nikkei.
All of the rights to the indices such as right to calculate, publicize, disseminate, and use
these indices are reserved by Nikkei.
Licensing agreement with Nikkei is necessary if companies intend to create Index - linked
funds and passive funds etc. It is also required to use this index for disseminating,providing, showing and etc. to the third party in the way as Nikkei decides.
(2)Risk
Nikkei calculates and publishes the Nikkei Stock Average Volatility Index in accordancewith the methods described in this document. In the event of circumstance not describedin this document, or if Nikkei determines it is impossible to use the methods described inthis document, Nikkei may use an alternative method of the index calculation as it deems
valid.
In case of a breakdown of computer system, natural disasters or any other unavoid ablesituations, Nikkei may postpone or cancel the calculation of the indices. Nikkei, under
any circumstance, does not guarantee the accuracy of these indices. Should any error in
the calculation of the index take place, Nikkei shall not be liable for any damages
sustained by any person or organization.
This document could be changed corresponding to the revision of the index calculation
rule etc in the future. Information expressed in this document is subject to change without
notice and in those cases Nikkei is under no obligation to update any recipien ts of thisdocument. Nikkei shall not accept any liability for any loss or damage arising from theusage of all or any part of this document.
(3)Corporation for the development of the index
In developing the Nikkei Stock Average Volatility Index, Nikkei ha s gained thecooperation of Quantitative Research Center of Nomura Securities CO., LTD. The
disclaimers in the above (2) are also applied to Quantitative Research Center of Nomura
Securities.

Copyright 2023 Nikkei Inc. All rights reserved.

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(4)ContactIndex Business Office, Nikkei Inc.
Mail: index@nex.nikkei.co.jpCopyright 2023 Nikkei Inc. All rights reserved.

6

Appendix : Change history of Index Guidebook
January 30, 2012 version

Initial version

February 9, 2012 version(deleted)

March 5, 2012 version

in “4: Calculation Example (in case of the closing(3:15:00pm) on November 1, 2011)”- modified the  values at the strike prices of 8500
and 8750 in the table of “(4) Calculation of thevariance of the underlying asset price derived fromthe prices of the selected near-term options(expiration month: Nov 2011)”- modified the number of decimal places of theAdjusted Value and a part of formula in the “(6)Calculate the adjusted value from option prices at thestrike price nearest from the future price for the nextterm; expiration month: Dec 2011”- modified the number of decimal places of the“Prices” at the strike price of 8750 in the table of“(7) Calculation of the variance of the underlying
asset price derived from the prices of the selected
next-term options (expiration month: Dec 2011)”

September 30, 2013 version

In “2:Index Calculation (3)Formula note(*7)”- modified the number of consecutive strike prices
from 3 to 6.

March 24, 2014 version

In “2:Index Calculation (1)Basic Points- modified the exchange name to “Osaka Exchange”
due to the trade name change.

December 13, 2021 version

In “2:Index Calculation (1)Basic Points”- Add the treatment for weekly options and on-demand
strike prices
In “2:Index Calculation (3)Formula”-

Change the interest rate from LIBOR to TORF

In

"3:Miscellaneous(1)PreviousandRetroactively

Calculation in the past"-Add the change in interest rate

Delete "4:Calculation Example"

May 29, 2023 version

In “2:Index Calculation (1)Basic Points”Copyright 2023 Nikkei Inc. All rights reserved.

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-Amend the description due to change in timing to rollto the next delivery month etc.
In “2:Index Calculation (3)Formula Note *7”- Amend the description due to the change ofdefinition of the target strike prices in the calculation

Copyright 2023 Nikkei Inc. All rights reserved.

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